Scenario 1: Performance problems only occur while HDT is running:
- Enable Windows Aero.
Scenario 2: Performance problems occur even if HDT is not running:
- HDT enables Hearthstones debug-logging "feature" (required to obtain any and all information)
- A lot is written to that log, apparently resulting in performance issues in some cases.
- A possible solution seems to be to set %USERPROFILE%\AppData\Local\Blizzard as an exception in Windows Defender. (source)
- If the previous one is not working there is no way around it, if you want to use HDT. The logging was not intended to be used in this way, so there will most likely never be a fix for it.
- So the only "fix" your FPS issues (you will no longer be able to use HDT): Close Hearthstone and HDT, then run the "HDTUninstaller.exe" found in the same folder. Click Hearthstone Logging: REMOVE. After restarting, your game should be back to normal, but running HDT again will re-enable the logging.